Problem: Simplify the following expression: $z = \dfrac{3r}{10} + \dfrac{r}{7}$
Explanation: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10$ and $7$ $\lcm(10, 7) = 70$ $ z = \dfrac{7}{7} \cdot \dfrac{3r}{10} + \dfrac{10}{10} \cdot \dfrac{r}{7} $ $z = \dfrac{21r}{70} + \dfrac{10r}{70}$ $z = \dfrac{21r +10r}{70}$ $z = \dfrac{31r}{70}$